Freeform surface off-axial three-mirror imaging system

ABSTRACT

A freeform surface off-axial three-mirror imaging system comprising a primary mirror, a secondary mirror, a tertiary mirror, and a detector. The secondary mirror comprises a first freeform surface and a second freeform surface. Each reflective surface of the primary mirror, the first freeform surface, the second freeform surface and the tertiary mirror is an xy polynomial freeform surface. The freeform surface off-axial three-mirror imaging system comprises a first effective focal length and a second effective focal length different from the first effective focal length.

CROSS-REFERENCE TO RELATED APPLICATIONS

The application is also related to copending applications entitled,“METHOD FOR DESIGNING FREEFORM SURFACE OFF-AXIAL THREE-MIRROR IMAGINGSYSTEM”, filed Jul. 3, 2019 (Ser. No. 16/502,148); “FREEFORM SURFACEOFF-AXIAL THREE-MIRROR IMAGING SYSTEM”, filed Jul. 3, 2019 (Ser. No.16/502,138); “FREEFORM SURFACE OFF-AXIAL THREE-MIRROR IMAGING SYSTEM”,filed Jul. 3, 2019 (Ser. No. 16/502,147).

FIELD

The subject matter herein generally relates to freeform surfaceoff-axial three-mirror imaging systems.

BACKGROUND

Compared with conventional rotationally symmetric surfaces, freeformsurfaces have asymmetric surfaces and more degrees of design freedom,which can reduce the aberrations and simplify the structure of thesystem. In recent years, freeform surfaces are often used in off-axialthree-mirror imaging system.

The conventional freeform surface off-axial three-mirror imaging systemsis working under an effective focal length (EFL), light from differentfields of view converge at different detectors with different locations.And, the detector at the same position can only observe objects in oneEFL.

BRIEF DESCRIPTION OF THE DRAWINGS

Implementations of the present technology will now be described, by wayof example only, with reference to the attached figures, wherein:

FIG. 1 is a light path schematic view of an embodiment of a freeformsurface off-axis three-mirror imaging system.

FIG. 2 shows a modulation-transfer-function (MTF) plot of an embodimentof a freeform surface off-axis three-mirror imaging system of oneembodiment when an aperture is located on a first freeform surface.

FIG. 3 shows a modulation-transfer-function (MTF) plot of a freeformsurface off-axis three-mirror imaging system of one embodiment when anaperture is located on a second freeform surface.

FIG. 4 shows a wave aberration diagram of an embodiment of a freeformsurface off-axis three-mirror imaging system of one embodiment when anaperture is located on a first curve surface.

FIG. 5 shows a wave aberration diagram of an embodiment of a freeformsurface off-axis three-mirror imaging system of one embodiment when anaperture is located on a second curve surface.

DETAILED DESCRIPTION

The disclosure is illustrated by way of example and not by way oflimitation in the figures of the accompanying drawings in which likereferences indicate similar elements. It should be noted that referencesto “another,” “an,” or “one” embodiment in this disclosure are notnecessarily to the same embodiment, and such references mean “at leastone.”

It will be appreciated that for simplicity and clarity of illustration,where appropriate, reference numerals have been repeated among thedifferent figures to indicate corresponding or analogous elements. Inaddition, numerous specific details are set forth in order to provide athorough understanding of the embodiments described herein. However, itwill be understood by those of ordinary skill in the art that theembodiments described herein can be practiced without these specificdetails. In other instances, methods, procedures and components have notbeen described in detail so as not to obscure the related relevantfeature being described. Also, the description is not to be consideredas limiting the scope of the embodiments described herein. The drawingsare not necessarily to scale and the proportions of certain parts havebeen exaggerated to better illustrate details and features of thepresent disclosure.

Several definitions that apply throughout this disclosure will now bepresented.

The term “contact” is defined as a direct and physical contact. The term“substantially” is defined to be that while essentially conforming tothe particular dimension, shape, or other feature that is described, thecomponent is not or need not be exactly conforming to the description.The term “comprising,” when utilized, means “including, but notnecessarily limited to”; it specifically indicates open-ended inclusionor membership in the so-described combination, group, series, and thelike.

Referring to FIG. 1, a freeform surface off-axial three-mirror imagingsystem 100 according to one embodiment is provided. The freeform surfaceoff-axial three-mirror imaging system 100 comprises a primary mirror102, a secondary mirror 104, an aperture 108, a tertiary mirror 110 anda detector 112. The secondary mirror 104 is an integrated mirror andcomprises a first freeform surface 104 a and a second freeform surface104 b integrated on a substrate. The aperture 108 is movable and capableof moving from the first freeform surface 104 a to the second freeformsurface 104 b. If the aperture 108 is located on the first freeformsurface 104 a, the freeform surface off-axial three-mirror imagingsystem 100 defines a first field of view and a first effective focallength (EFL). If the aperture 108 is located on the second freeformsurface 104 b, the freeform surface off-axial three-mirror imagingsystem 100 defines a second field of view and a second EFL. A surfaceshape of each of the primary mirror 102, the secondary mirror 104, andthe tertiary mirror 110 is a freeform surface. The feature rays exitingfrom the light source would be successively reflected by the primarymirror 102, the secondary mirror 104 and the tertiary mirror 110 to forman image on an detector 112.

A first three-dimensional rectangular coordinates system (X,Y,Z) isdefined by a location of the primary mirror 102; a secondthree-dimensional rectangular coordinates system (X′,Y′,Z′) is definedby a location of the first freeform surface 104 a; a thirdthree-dimensional rectangular coordinates system (X″,Y″,Z″) is definedby a location of the second freeform surface 104 b; and a fourththree-dimensional rectangular coordinates system (X′″,Y′″,Z′″) isdefined by a location of the tertiary mirror 110.

A vertex of the primary mirror 102 is an origin of the firstthree-dimensional rectangular coordinates system (X,Y,Z). A horizontalline passing through the vertex of the primary mirror 102 is defined asan Z-axis; in the Z-axis, to the left is negative, and to the right ispositive. A Y-axis is substantially perpendicular to the Z-axis and in aplane shown in FIG. 1; in the Y-axis, to the upward is positive, and tothe downward is negative. An X-axis is substantially perpendicular to aYZ plane; in the X-axis, to the inside is positive, and to the outsideis negative.

A reflective surface of the primary mirror 102 in the firstthree-dimensional rectangular coordinates system (X,Y,Z) is an xypolynomial freeform surface; and an xy polynomial equation can beexpressed as follows:

${z\left( {x,y} \right)} = {\frac{c\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k} \right){c^{2}\left( {x^{2} + y^{2}} \right)}}}} + {\sum\limits_{i = 1}^{N}{A_{i}x^{m}{y^{n}.}}}}$

In the xy polynomial equation, z represents surface sag, c representssurface curvature, k represents conic constant, while A_(i) representsthe ith term coefficient. Since the freeform surface off-axialthree-mirror imaging system 100 is symmetrical about a YOZ plane, soeven order terms of x can be only remained. At the same time, higherorder terms will increase the fabrication difficulty of the off-axialthree-mirror optical system with freeform surfaces 100. In oneembodiment, the reflective surface of the primary mirror 102 is afourth-order polynomial freeform surface of xy without odd items of x;and an equation of the fourth-order polynomial freeform surface of xycan be expressed as follows:

${z\left( {x,y} \right)} = {\frac{c\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k} \right){c^{2}\left( {x^{2} + y^{2}} \right)}}}} + {A_{2}y} + {A_{3}x^{2}} + {A_{5}y^{2}} + {A_{7}x^{2}y} + {A_{9}y^{3}} + {A_{10}x^{4}} + {A_{12}x^{2}y^{2}} + {A_{14}y^{4}} + {A_{16}x^{4}y} + {A_{18}x^{2}{y^{3}.}}}$

In one embodiment, the values of c, k, and A_(i) in the equation of theeighth-order polynomial freeform surface of xy of the reflective surfaceof the primary mirror 102 are listed in TABLE 1. However, the values ofc, k, and A_(i) in the eighth order xy polynomial equation are notlimited to TABLE 1.

TABLE 1 c −5.8323994031E−04 Conic Constant (k) −9.9850764719E−01 A₂  1.2842483202E+00 A₃ −2.2637598437E−04 A₅ −1.2187168002E−03 A₇  1.3798242519E−05 A₉   5.0401995782E−06 A₁₀ −6.8791876162E−09 A₁₂−7.9586143947E−08 A₁₄   1.3200240494E−07 A₁₆   6.9303940947E−10 A₁₈  3.1467633702E−09

A vertex of the first freeform surface 104 a is an origin of the secondthree-dimensional rectangular coordinates system (X′,Y′,Z′). The secondthree-dimensional rectangular coordinates system (X′,Y′,Z′) is obtainedby moving the first three-dimensional rectangular coordinates system(X,Y,Z) along an Z-axis negative direction and a Y-axis positivedirection. In one embodiment, The second three-dimensional rectangularcoordinates system (X′,Y′,Z′) is obtained by moving the firstthree-dimensional rectangular coordinates system (X,Y,Z) for about154.876 mm along the Y-axis positive direction, and then moving forabout 134.412 mm along the Z-axis negative direction, and then rotatingalong the counterclockwise direction for about 69.835° with the X axisas the rotation axis. A distance between the origin of the firstthree-dimensional rectangular coordinates system (X,Y,Z) and the originof the second three-dimensional rectangular coordinates system(X′,Y′,Z′) is about 205.068 mm.

In the second three-dimensional rectangular coordinates system(X′,Y′,Z′), a reflective surface of the first freeform surface 104 a isan x′y′ polynomial freeform surface. An x′y′ polynomial surface equationcan be expressed as follows:

${z^{\prime}\left( {x^{\prime},y^{\prime}} \right)} = {\frac{c^{\prime}\left( {x^{\prime 2} + y^{\prime 2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{\prime}} \right){c^{\prime 2}\left( {x^{\prime 2} + y^{\prime 2}} \right)}}}} + {\sum\limits_{i = 1}^{N}{A_{i}^{\prime}x^{\prime\; m}y^{\prime\; n}}}}$

In the x′y′ polynomial freeform surface equation, z′ represents surfacesag, c′ represents surface curvature, k′ represents conic constant,while A_(i)′ represents the ith term coefficient. Since the freeformsurface off-axial three-mirror imaging system 100 is symmetrical aboutY′Z′ plane, so even-order terms of x′ can be only remained. At the sametime, higher order terms will increase the fabrication difficulty of thefreeform surface off-axial three-mirror imaging system 100. In oneembodiment, the reflective surface of the first freeform surface 104 ais a fourth-order polynomial freeform surface of x′y′ without odd itemsof x′. An equation of the fourth-order polynomial freeform surface ofx′y′ can be expressed as follows:

${z^{\prime}\left( {x^{\prime},y^{\prime}} \right)} = {\frac{c^{\prime}\left( {x^{\prime 2} + y^{\prime 2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{\prime}} \right){c^{\prime 2}\left( {x^{\prime 2} + y^{\prime 2}} \right)}}}} + {A_{2}^{\prime}y^{\prime}} + {A_{3}^{\prime}x^{\prime 2}} + {A_{5}^{\prime}y^{\prime 2}} + {A_{7}^{\prime}x^{\prime 2}y^{\prime}} + {A_{9}^{\prime}y^{\prime 3}} + {A_{10}^{\prime}x^{\prime 4}} + {A_{12}^{\prime}x^{\prime 2}y^{\prime 2}} + {A_{14}^{\prime}y^{\prime 4}} + {A_{16}^{\prime}x^{\prime 4}y^{\prime}} + {A_{18}^{\prime}x^{\prime 2}y^{\prime 3}}}$

In one embodiment, the values of c′, k′, and A_(i)′ in the equation ofthe eighth-order polynomial freeform surface of x′y′ are listed in TABLE2. However, the values of c′, k′, and A_(i)′ in the equation of theeighth-order polynomial freeform surface of x′y′ are not limited toTABLE 2.

TABLE 2 c′   2.9050135953E−03 Conic Constant (k′) −2.0000000000E+01 A₂′−4.1074509329E−01 A₃′ −2.0823946458E−03 A₅′ −2.6447846390E−03 A₇′  2.7184263806E−05 A₉′   1.2986485221E−05 A₁₀′   4.1507879401E−08 A₁₂′  8.4956081916E−08 A₁₄′   2.5155613779E−08 A₁₆′   9.3423798571E−10 A₁₈′  1.7086690206E−09

A vertex of the second freeform surface 104 b is an origin of the thirdthree-dimensional rectangular coordinates system (X″,Y″,Z″). The thirdthree-dimensional rectangular coordinates system (X″,Y″,Z″) is obtainedby moving the second three-dimensional rectangular coordinates system(X′,Y′,Z′) along an Z′-axis positive direction and a Y′-axis negativedirection. In one embodiment, the third three-dimensional rectangularcoordinates system (X″,Y″,Z″) is obtained by moving the secondthree-dimensional rectangular coordinates system (X′,Y′,Z′) for about2.863 mm along a Y′-axis negative direction, and then moving for about12.739 mm along an Z′-axis negative direction, and then rotating alongthe counterclockwise direction for about 3.636° with the X′ axis as therotation axis. A distance between the origin of the secondthree-dimensional rectangular coordinates system (X′,Y′,Z′) and theorigin of the third three-dimensional rectangular coordinates system(X″,Y″,Z″) is about 13.057 mm.

In the third three-dimensional rectangular coordinates system(X″,Y″,Z″), a reflective surface of the second freeform surface 104 b isan x″y″ polynomial freeform surface. An x″y″ polynomial surface equationcan be expressed as follows:

${z^{''}\left( {x^{''},y^{''}} \right)} = {\frac{c^{''}\left( {x^{''2} + y^{''\; 2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{''}} \right){c^{''2}\left( {x^{''2} + y^{\prime^{\prime}2}} \right)}}}} + {\sum\limits_{i = 1}^{N}{A_{i}^{''}x^{''\; m}y^{''\; n}}}}$

In the x″y″ polynomial freeform surface equation, z″ represents surfacesag, c″ represents surface curvature, k″ represents conic constant,while A_(i)″ represents the ith term coefficient. Since the freeformsurface off-axial three-mirror imaging system 100 is symmetrical aboutY″Z″ plane, so even-order terms of x″ can be only remained. At the sametime, higher order terms will increase the fabrication difficulty of thefreeform surface off-axial three-mirror imaging system 100. In oneembodiment, the reflective surface of the second freeform surface 104 bis a fourth-order polynomial freeform surface of x″y″ without odd itemsof x″. An equation of the fourth-order polynomial freeform surface ofx″y″ can be expressed as follows:

${z^{''}\left( {x^{''},y^{''}} \right)} = {\frac{c^{''}\left( {x^{''2} + y^{''2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{''}} \right){c^{''2}\left( {x^{''2} + y^{''2}} \right)}}}} + {A_{2}^{''}y^{''}} + {A_{3}^{''}x^{''2}} + {A_{5}^{''}y^{''2}} + {A_{7}^{''}x^{''2}y^{''}} + {A_{9}^{''}y^{''3}} + {A_{10}^{''}x^{''4}} + {A_{12}^{''}x^{''2}y^{''2}} + {A_{14}^{''}y^{''4}} + {A_{16}^{''}x^{''4}y^{''}} + {A_{18}^{''}x^{''2}y^{''3}}}$

In one embodiment, the values of c″, k″, and A_(i)″ in the equation ofthe eighth-order polynomial freeform surface of x″y″ are listed in TABLE3. However, the values of c″, k″, and A in the equation of theeighth-order polynomial freeform surface of x″y″ are not limited toTABLE 3.

TABLE 3 c″ −1.7198715496E−03 Conic Constant (k″) −2.0000000000E+01 A₂″−2.8476156510E−01 A₃″ −8.1816431466E−06 A₅″ −6.1295856898E−04 A₇″  2.4682320767E−05 A₉″   1.1543822730E−05 A₁₀″ −2.9325409902E−08 A₁₂″−6.4494233230E−08 A₁₄″ −3.9424838348E−08 A₁₆″   7.3676644654E−11 A₁₈″−1.6543729895E−10

The aperture 108 includes a circular through hole with a radius of about10.576 mm. In one embodiment, a central of the first field of view is0°, and a range of the field of view is 2°×2°, the first EFL is 120 mm;a central of the second field of view is 4°, a range of the second fieldof view is 1.71°×1.71°, the second EFL is 140 mm. The aperture 108 iscapable of moving between the center of the second three-dimensionalcoordinate system and the center of the third three-dimensionalcoordinate system.

A vertex of the tertiary mirror 110 is an origin of the fourththree-dimensional rectangular coordinates system (X′″,Y′″,Z′″). Thefourth three-dimensional rectangular coordinates system (X′″,Y′″,Z′″) isobtained by moving the first three-dimensional rectangular coordinatessystem (X,Y,Z) along an Z-axis negative direction and a Y-axis negativedirection. In one embodiment, the fourth three-dimensional rectangularcoordinates system (X′″,Y′″,Z′″) is obtained by moving the firstthree-dimensional rectangular coordinates system (X,Y,Z) for about123.525 mm along the Z-axis negative direction, and then moving forabout 18.584 mm along the Y-axis negative direction, and then rotatingalong the counterclockwise direction for about 71.121° with the X-axis sas the rotation axis. A distance between the origin of the fourththree-dimensional rectangular coordinates system (X′″,Y′″,Z′″) and theorigin of the first three-dimensional rectangular coordinates system(X,Y,Z) is about 124.915 mm.

In the fourth three-dimensional rectangular coordinates system(X′″,Y′″,Z′″), a reflective surface of the tertiary mirror 110 is anx′″y′″ polynomial freeform surface. An x′″y′″ polynomial surfaceequation can be expressed as follows:

${z^{\prime\prime\prime}\left( {x^{\prime\prime\prime},y^{\prime\prime\prime}} \right)} = {\frac{c^{\prime\prime\prime}\left( {x^{\prime\prime\prime 2} + y^{\prime\prime\prime 2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{\prime\prime\prime}} \right){c^{\prime\prime\prime 2}\left( {x^{\prime\prime\prime 2} + y^{{\prime\prime\prime}^{\prime}2}} \right)}}}} + {\sum\limits_{i = 1}^{N}{A_{i}^{\prime\prime\prime}x^{{\prime\prime\prime}\; m}{y^{{\prime\prime\prime}\; n}.}}}}$

In the x′″y′″ polynomial freeform surface equation, z′″ representssurface sag, c′″ represents surface curvature, k′″ represents conicconstant, while A₁′″ represents the ith term coefficient. Since thefreeform surface off-axial three-mirror imaging system 100 issymmetrical about Y′″Z′″ plane, so even-order terms of x′″ can be onlyremained. At the same time, higher order terms will increase thefabrication difficulty of the freeform surface off-axial three-mirrorimaging system 100. In one embodiment, the reflective surface of thetertiary mirror 110 is a fourth-order polynomial freeform surface ofx′″y′″ without odd items of x′″. An equation of the fourth-orderpolynomial freeform surface of x′″y′″ can be expressed as follows:

${z^{\prime\prime\prime}\left( {x^{\prime\prime\prime},y^{\prime\prime\prime}} \right)} = {\frac{c^{\prime\prime\prime}\left( {x^{\prime\prime\prime 2} + y^{\prime\prime\prime 2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{\prime\prime\prime}} \right){c^{\prime\prime\prime 2}\left( {x^{\prime\prime\prime 2} + y^{\prime\prime\prime 2}} \right)}}}} + {A_{2}^{\prime\prime\prime}y^{\prime\prime\prime}} + {A_{3}^{\prime\prime\prime}x^{\prime\prime\prime 2}} + {A_{5}^{\prime\prime\prime}y^{\prime\prime\prime 2}} + {A_{7}^{\prime\prime\prime}x^{\prime\prime\prime 2}y^{\prime\prime\prime}} + {A_{9}^{\prime\prime\prime}y^{\prime\prime\prime 3}} + {A_{10}^{\prime\prime\prime}x^{\prime\prime\prime 4}} + {A_{12}^{\prime\prime\prime}x^{\prime\prime\prime 2}y^{\prime\prime\prime 2}} + {A_{14}^{\prime\prime\prime}y^{\prime\prime\prime 4}} + {A_{16}^{\prime\prime\prime}x^{\prime\prime\prime 4}y^{\prime\prime\prime}} + {A_{18}^{\prime\prime\prime}x^{\prime\prime\prime 2}{y^{\prime\prime\prime 3}.}}}$

In one embodiment, the values of c′″, k′″, and A_(i)′″ in the eighthorder x′″y′″ polynomial surface equation are listed in TABLE 4. However,the values of c′″, k′″, and A_(i)′″ in the fourth order x′″y′″polynomial surface equation are not limited to TABLE 4.

TABLE 4 c″′ −4.7284759870E−03 Conic Constant (k″′) −1.0000000076E+00A₂″′ −4.1466998089E−02 A₃″′   4.4881747268E−05 A₅″′ −2.0982402779E−04A₇″′   4.6762991642E−06 A₉″′   1.4560243304E−06 A₁₀″′ −1.1651173535E−08A₁₂″′ −2.1669621957E−08 A₁₄″′ −8.9614302576E−09 A₁₆″′   1.2786423942E−10A₁₈″′   2.6054503418E−10

The materials of the primary mirror 102, the secondary mirror 104 andthe tertiary mirror 110 can be aluminum, beryllium or other metals. Thematerials of the primary mirror 102, the secondary mirror 104 and thetertiary mirror 110 can also be silicon carbide, quartz or otherinorganic materials. A reflection enhancing coating can also be coatedon the metals or inorganic materials to enhance the reflectivityperformance of the three mirrors. In one embodiment, the reflectionenhancing coating is a gold film. A size of each of the primary mirror102, the secondary mirror 104 and the tertiary mirror 110 can bedesigned according to actual needs.

In the fourth three-dimensional rectangular coordinates system(X′″,Y′″,Z′″), a distance along the Z′″-axis negative direction betweena center of the detector 112 and the vertex of the tertiary mirror 110is about 158.283 mm. The center of the detector 112 deviates from theZ′″ axis in the positive direction of the Y′″ axis, and a deviation isabout 17.259 mm. An angle of the detector with the X′″Y′″ plane in theclockwise direction is about 6.568°. A size of the detector 112 can beselected according to actual needs.

An effective entrance pupil diameter of a first field of view passage ora second field view of passage of the freeform surface off-axialthree-mirror imaging system 100 is about 20 mm.

The freeform surface off-axial three-mirror imaging system 100 adopts anoff-axis field of view in meridian direction. In one embodiment, acenter of the first field of view is 0°, and a range of the first fieldof view is 2°×2°, wherein the range of the first field of view in thesagittal direction is −1° to 1°, the range of the first field of view inthe meridional direction is −1° to 1°, the FOL is 120 mm. A center ofthe second field of view is 4°, and a range of the second field of viewis 1.71°×1.71°, wherein the range of the second field of view in thesagittal direction is 3.145° to 4.855°, and the range of the secondfield of view in the meridional direction is −0.855° to 0.855°.

A wavelength of the freeform surface off-axial three-mirror imagingsystem 100 is not limited, in one embodiment, the wavelength of thefreeform surface off-axial three-mirror imaging system 100 is from about400 nm to about 700 nm.

A modulation transfer functions (MTF) of the freeform surface off-axialthree-mirror imaging system 100 in visible band of different field ofview is separately shown in FIGS. 2 and 3. In FIG. 2, the aperture 108is located on the first freeform surface 104 a, and the EFL is 120 mm.In FIG. 3, the aperture 108 is located on the second freeform surface104 b, and the EFL is 140 mm. FIGS. 2 and 3 both show that an imagingquality of the freeform surface off-axial three-mirror imaging system100 is high.

FIGS. 4 and 5 superlatively shows a wave aberration diagram of anembodiment of the freeform surface off-axis three-mirror imaging system100. In FIG. 4, the aperture 108 is located on the first freeformsurface 104 a, and the EFL is 120 mm. In FIG. 5, the aperture 108 islocated on the second freeform surface 104 b, and the EFL is 140 mm. Inthe two different working states shown in FIGS. 4 and 5, the averagevalue of the wave aberration is less than 0.034λ, where λ=546.1 nm. Theimaging quality of the freeform surface off-axis three-mirror imagingsystem 100 is good.

The freeform off-axis three-mirror imaging system 100 provided by thepresent invention adopts an off-axis three-reverse system, and has nocentral obscuration. The freeform off-axis three-mirror imaging system100 has two different fields of view, and objects of the two differentfields of view are imaged at the same detector 112; The freeformoff-axis three-mirror imaging system 100 has an F-number of 6, whichenable the freeform off-axis three-mirror imaging system 100 has ahigh-resolution image. Further, the structure of the freeform off-axisthree-mirror imaging system 100 is compact.

The applications of the freeform surface off-axial three-mirror imagingsystem 100 comprises earth observation, space target detection,astronomical observations, Multi-spectral thermal imaging, anddimensional mapping.

Depending on the embodiment, certain blocks/steps of the methodsdescribed may be removed, others may be added, and the sequence ofblocks may be altered. It is also to be understood that the descriptionand the claims drawn to a method may comprise some indication inreference to certain blocks/steps. However, the indication used is onlyto be viewed for identification purposes and not as a suggestion as toan order for the blocks/steps.

The embodiments shown and described above are only examples. Even thoughnumerous characteristics and advantages of the present technology havebeen set forth in the foregoing description, together with details ofthe structure and function of the present disclosure, the disclosure isillustrative only, and changes may be made in the detail, especially inmatters of shape, size, and arrangement of the parts within theprinciples of the present disclosure, up to and including the fullextent established by the broad general meaning of the terms used in theclaims. It will therefore be appreciated that the embodiments describedabove may be modified within the scope of the claims.

What is claimed is:
 1. A freeform surface off-axial three-mirror imagingsystem, comprising: a primary mirror, a first three-dimensionalrectangular coordinates system (X,Y,Z) is defined with a vertex of theprimary mirror as a first origin, and in the first three-dimensionalrectangular coordinates system (X,Y,Z), a reflective surface of theprimary mirror is an xy polynomial freeform surface; a secondary mirrorcomprising a first freeform surface and a second freeform surface, asecond three-dimensional rectangular coordinates system (X′,Y′,Z′) isdefined with a vertex of the first freeform surface as a second origin,and the second three-dimensional rectangular coordinates system(X′,Y′,Z′) is obtained by moving the first three-dimensional rectangularcoordinates system (X,Y,Z) along an Z-axis negative direction and aY-axis positive direction, and in the second three-dimensionalrectangular coordinates system (X′,Y′,Z′), a reflective surface of thefirst freeform surface is an x′y′ polynomial freeform surface; a thirdthree-dimensional rectangular coordinates system (X″,Y″,Z″) is definedwith a vertex of the second freeform surface as a third origin, and thethird three-dimensional rectangular coordinates system (X″,Y″,Z″) isobtained by moving the second three-dimensional rectangular coordinatessystem (X′,Y′,Z′) along an Z-axis positive direction and a Y-axisnegative direction, and in the third three-dimensional rectangularcoordinates system (X″,Y″,Z″), a reflective surface of the secondfreeform surface is an x″y″ polynomial freeform surface; an aperturebeing capable of moving between the first freeform surface and thesecond freeform surface, wherein when the aperture is located on thefirst freeform surface, the freeform surface off-axial three-mirrorimaging system comprises a first effective focal length; when theaperture is located on the second freeform surface, the freeform surfaceoff-axial three-mirror imaging system comprises a second effective focallength different from the first effective focal length; a tertiarymirror, a fourth three-dimensional rectangular coordinates system(X′″,Y′″,Z′″) is defined with a vertex of the tertiary mirror as afourth origin, and the fourth three-dimensional rectangular coordinatessystem (X′″,Y′″,Z′″) is obtained by moving the first three-dimensionalrectangular coordinates system (X,Y,Z) along an Z-axis negativedirection and a Y-axis negative direction, and in the fourththree-dimensional rectangular coordinates system (X′″,Y′″,Z′″), areflective surface of the tertiary mirror is an x′″y′″ polynomialfreeform surface; a detector, feature rays is reflected by the primarymirror, the secondary mirror and the tertiary mirror to form an image onthe detector; wherein the freeform surface off-axial three-mirrorimaging system comprises a first field of view formed by the firstfreeform surface and a second field of view formed by the secondfreeform surface.
 2. The freeform surface off-axial three-mirror imagingsystem of claim 1, wherein the second three-dimensional rectangularcoordinates system (X′,Y′,Z′) is obtained by moving the firstthree-dimensional rectangular coordinates system (X,Y,Z) forapproximately 154.876 mm along the Y-axis positive direction, and thenmoving for approximately 134.412 mm along the Z-axis negative direction,and then rotating along the counterclockwise direction for approximately69.835° with the X axis as the rotation axis.
 3. The freeform surfaceoff-axial three-mirror imaging system of claim 1, wherein a distancebetween the origin of the first three-dimensional rectangularcoordinates system (X,Y,Z) and the origin of the secondthree-dimensional rectangular coordinates system (X′,Y′,Z′) isapproximately 205.068 mm.
 4. The freeform surface off-axial three-mirrorimaging system of claim 1, wherein the third three-dimensionalrectangular coordinates system (X″,Y″,Z″) is obtained by moving thesecond three-dimensional rectangular coordinates system (X′,Y′,Z′) forapproximately 2.863 mm along a Y′-axis negative direction, and thenmoving for approximately 12.739 mm along an Z′-axis negative direction,and then rotating along the counterclockwise direction for approximately3.636° with the X′ axis as the rotation axis.
 5. The freeform surfaceoff-axial three-mirror imaging system of claim 1, wherein a distancebetween the origin of the second three-dimensional rectangularcoordinates system (X′,Y′,Z′) and the origin of the thirdthree-dimensional rectangular coordinates system (X″,Y″,Z″) isapproximately 13.057 mm.
 6. The freeform surface off-axial three-mirrorimaging system of claim 1, wherein the fourth three-dimensionalrectangular coordinates system (X′″,Y′″,Z′″) is obtained by moving thefirst three-dimensional rectangular coordinates system (X,Y,Z) forapproximately 123.525 mm along the Z-axis negative direction, and thenmoving for approximately 18.584 mm along the Y-axis negative direction,and then rotating along the counterclockwise direction for approximately71.121° with the X-axis as the rotation axis.
 7. The freeform surfaceoff-axial three-mirror imaging system of claim 1, a distance between theorigin of the fourth three-dimensional rectangular coordinates system(X′″,Y′″,Z′″) and the origin of the first three-dimensional rectangularcoordinates system (X,Y,Z) is approximately 124.915 mm.
 8. The freeformsurface off-axial three-mirror imaging system of claim 1, wherein thereflective surface of the primary mirror is a fourth-order polynomialfreeform surface of xy without odd items of x; and an equation of theeighth-order polynomial freeform surface of xy can be expressed asfollows:${z\left( {x,y} \right)} = {\frac{c\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k} \right){c^{2}\left( {x^{2} + y^{2}} \right)}}}} + {A_{2}y} + {A_{3}x^{2}} + {A_{5}y^{2}} + {A_{7}x^{2}y} + {A_{9}y^{3}} + {A_{10}x^{4}} + {A_{12}x^{2}y^{2}} + {A_{14}y^{4}} + {A_{16}x^{4}y} + {A_{18}x^{2}y^{3}}}$wherein z represents surface sag, c represents surface curvature, krepresents conic constant, and A_(i) represents the ith termcoefficient.
 9. The freeform surface off-axial three-mirror imagingsystem of claim 8, wherein c=−5.8323994031E−04, k=−9.9850764719E−01,A₂=1.2842483202E+00, A₃=−2.2637598437E−04, A₅=−1.2187168002E−03,A₇=1.3798242519E−05, A₉=5.0401995782E−06, A₁₀=−6.8791876162E−09,A₁₂=−7.9586143947E−08, A₁₄=1.3200240494E−07, A₁₆=6.9303940947E−10,A₁₈=3.1467633702E−09.
 10. The freeform surface off-axial three-mirrorimaging system of claim 1, wherein in the second three-dimensionalrectangular coordinates system (X′,Y′,Z′), the reflective surface of thesecondary mirror is an fourth-order polynomial freeform surface of x′y′without odd items of x′, and an equation of the eighth-order polynomialfreeform surface of x′y′ is:${{z^{\prime}\left( {x^{\prime},y^{\prime}} \right)} = {\frac{c^{\prime}\left( {x^{\prime 2} + y^{\prime 2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{\prime}} \right){c^{\prime 2}\left( {x^{\prime 2} + y^{\prime 2}} \right)}}}} + {A_{2}^{\prime}y^{\prime}} + {A_{3}^{\prime}x^{\prime 2}} + {A_{5}^{\prime}y^{\prime 2}} + {A_{7}^{\prime}x^{\prime 2}y^{\prime}} + {A_{9}^{\prime}y^{\prime 3}} + {A_{10}^{\prime}x^{\prime 4}} + {A_{12}^{\prime}x^{\prime 2}y^{\prime 2}} + {A_{14}^{\prime}y^{\prime 4}} + {A_{16}^{\prime}x^{\prime 4}y^{\prime}} + {A_{18}^{\prime}x^{\prime 2}y^{\prime 3}}}},$wherein z′ represents surface sag, c′ represents surface curvature, k′represents conic constant, and A_(i)′ represents the ith termcoefficient.
 11. The freeform surface off-axial three-mirror imagingsystem of claim 10, wherein c′=2.9050135953E−03, k′=−2.0000000000E+01,A₂′=−4.1074509329E−01, A₃′=−2.0823946458E−03, A₅′=−2.6447846390E−03,A₇′=2.7184263806E−05, A₉′=1.2986485221E−05, A₁₀′=4.1507879401E−08,A₁₂′=8.4956081916E−08, A₁₄′=2.5155613779E−08, A₁₆′=9.3423798571E−10,A₁₈′=1.7086690206E−09.
 12. The freeform surface off-axial three-mirrorimaging system of claim 1, wherein in the third three-dimensionalrectangular coordinates system (X″,Y″,Z″), the reflective surface of thetertiary mirror is an fourth-order polynomial freeform surface of x″y″without odd items of x″, and an equation of the eighth-order polynomialfreeform surface of x″y″ is${z^{''}\left( {x^{''},y^{''}} \right)} = {\frac{c^{''}\left( {x^{''2} + y^{''2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{''}} \right){c^{''2}\left( {x^{''2} + y^{''2}} \right)}}}} + {A_{2}^{''}y^{''}} + {A_{3}^{''}x^{''2}} + {A_{5}^{''}y^{''2}} + {A_{7}^{''}x^{''2}y^{''}} + {A_{9}^{''}y^{''3}} + {A_{10}^{''}x^{''4}} + {A_{12}^{''}x^{''2}y^{''2}} + {A_{14}^{''}y^{''4}} + {A_{16}^{''}x^{''4}y^{''}} + {A_{18}^{''}x^{''2}y^{''3}}}$wherein z″ represents surface sag, c″ represents surface curvature, k″represents conic constant, and A_(i)″ represents the ith termcoefficient.
 13. The freeform surface off-axial three-mirror imagingsystem of claim 12, wherein c″=−1.7198715496E−03, k″=−2.0000000000E+01,A₂″=−2.8476156510E−01, A₃″=−8.1816431466E−06, A₅″=−6.1295856898E−04,A₇″=2.4682320767E−05, A₉″=1.1543822730E−05, A₁₀″=−2.9325409902E−08,A₁₂″=−6.4494233230E−08, A₁₄″=−3.9424838348E−08, A₁₆″=7.3676644654E−11,A₁₈″=−1.6543729895E−10.
 14. The freeform surface off-axial three-mirrorimaging system of claim 1, wherein in the fourth three-dimensionalrectangular coordinates system (X′″,Y′″,Z′″), a distance along theZ′″-axis negative direction between a center of the detector and thevertex of the tertiary mirror is approximately 124.915 mm.
 15. Thefreeform surface off-axial three-mirror imaging system of claim 1,wherein an effective the freeform surface off-axial three-mirror imagingsystem is approximately 20 mm.
 16. The freeform surface off-axialthree-mirror imaging system of claim 1, wherein a center of the firstfield of view is 0°, and a range of the first field of view is 2°×2°.17. The freeform surface off-axial three-mirror imaging system of claim1, wherein the first effective focal length is 120 mm.
 18. The freeformsurface off-axial three-mirror imaging system of claim 1, wherein acenter of the second field of view is 4°, and a range of the secondfield of view is 2°×2°.
 19. The freeform surface off-axial three-mirrorimaging system of claim 18, wherein the range of the second field ofview in the sagittal direction is 3° to 5°, and the range of the secondfield of view in the meridional direction is −1° to 1°.
 20. The freeformsurface off-axial three-mirror imaging system of claim 1, wherein thesecond effective focal length is 140 mm.